PHYS345 Electricity and Electronics

Quiz 4: ac Circuit Analysis

Problem 4-46

Find the voltage across the capacitor.

Evaluation of the Element Reactances:

Conversion of L and C to reactances

Circuit Reduction:

This is a simple circuit, meaning that the network of passive elements may be reduced to a single equivalent impedance. The progression to the simple circuit is indicated below.

Circuit reduction: series elements
Circuit reduction: parallel elements
Circuit reduction: series elements

Evaluation of Source Current:

The equivalent impedance is Zeq = (9+j9) ohm = 12.7 ohm \/ -45 deg.

The source current is is = vs /Zeq = (36 V) / (12.7 ohm \/ -45) = 2.83 A \/ -45 deg.

Evaluation of the Voltage across the Element:

Note that at the node, the current splits equally since the two parallel branches have the same impedance. Thus the current through the capacitor is ic = 1.42 A \/ -45 deg. Consequently the voltage across the capacitor is vc = icZc = (1.42 A \/ -45)(6 ohm \/ -90) = 8.52 V \/ -135 deg.

Last updated Oct. 1, 1999.
Copyright George Watson, Univ. of Delaware, 1999.